• Wave Nature of Light

• Quantized Energy and Photons

• Bohr Model of the Atom

• Wave Behavior of Matter

• Quantum Mechanics / Atomic Orbitals

• Shapes of Orbitals

• Multi-electron Atoms

• Electron configurations and the periodic table

• To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation.

• The height of the wave is amplitude (A).

• The distance between corresponding points on adjacent waves is the wavelength (, “lambda”),typically in units of meters.

Section 6

.1

• The number of waves passing a given point per

unit of time is the frequency (, “nu”) in units of s–1.

• For waves traveling at the same velocity, the

longer the wavelength, the smaller the frequency

(and vice versa).

Higher Frequency

Lower Frequency

Section 6

.1

• All electromagnetic radiation travels at the same

velocity: the speed of light (c), 3.00 108 m/s.

• Therefore, c = or = c/ or = c/

Section 6

.1

• The wave nature of light

does not explain how an

object can glow when its

temperature increases.

• Max Planck explained it

by assuming that energy

comes in packets of

matter called quanta.

Section 6

.2

Max Plank received the Nobel Prize in Physics for the quantum

theory in 1918.

• Planks proposed a

quantum of energy was

related to frequency:

Section 6

.2

E = h h=Plank’s constant

= 6.626x10-34 Js

= frequency (s-1)

• The idea is that energy

can be emitted or

absorbed only in integer

multiples of the frequency

(h, 2h, 3h, etc)

Continuous energy

Quantized energy

• Einstein used this assumption to explain the photoelectric effect.

• He showed photon’s energy is proportional to its frequency:

E = h

h = Planck’s constant = 6.63 10−34 J·s

(energy is in J)

Albert Einstein received the Nobel Prize in Physics

for the photoelectric effect, not for relativity (E=mc2).

Section 6

.2

So, if the wavelength of light is

known, one can calculate the

energy in one photon, or

quanta, of that light:

c = and E = h

E = hc/

Q: But photons have mass, so is

light a particle or is it a wave?

A: Yes!

This paradox is called wave-particle duality.

Section 6

.2

Researchers at Ecole

Polytechnique Federale

de Lausanne (EPFL)

have captured light

behaving as a wave and

a particle at the same

time!

http://actu.epfl.ch/news/t

he-first-ever-photograph-

of-light-as-both-a-parti/

https://www.youtube.com/watch?t=46&v=mlaVHxUSiNk

– Calculate the frequency of laser radiation which

has a wavelength (l) of 640.0 nm.

– Calculate the wavelength of radio waves with a

frequency of 103.4 MHz (1 MHz = 1 × 106 s–1).

Section 6

.2

– What is the energy of one photon of radiation

with a frequency of 4.69 × 1014 s–1?

– What is the total energy of a pulse of 5.0 × 1017

photons at this frequency?

Section 6

.2

• If a laser emits 1.3 × 10–2 J of energy, how many

photons were emitted?

Section 6

.2

Another mystery involved the emission spectra

observed from energy emitted by atoms and

molecules.

Section 6

.3

• White light sources produce

a continuous spectrum.

• Atoms and molecules only

produce a line spectrum of

discrete wavelengths.

Section 6

.3

Niels Bohr’s explanation:

1. Electrons in an atom can only orbit at certain radii, corresponding to specific energies.

Section 6

.3

E = h h = Planck’s constant

= frequency of radiation

2. Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.

3. Energy is only absorbed or emitted as an electron moves from one “allowed” energy state to another; the energy is defined by:

n=1

n=2

n=3

n=4

Energy that’s absorbed (promotion) or emitted (demotion) can be calculated by the Rydberg equation:

RH = Rydberg constant, 1.097 107 m–1

h = Planck’s constant; c = speed of light

ni = initial energy level of electron

nf = final energy level of the electron

22

11

if

Hnn

hcRE

22

18 111018.2

if nnxE

Section 6

.3

+ -

• Moving from high n to lower n

– nf< ni so E<0

– Emits energy

• Moving from low n to higher n

– nf > ni so E > 0

– Absorbs energy

22

11

if

Hnn

hcRE

Section 6

.3

Ground State = lowest energy state

Excited State = higher energy state

• Strengths of the Bohr model:

– Electrons have discrete energies

– Energy is absorbed or radiated when electrons are moved between discrete levels

• Limitations of the model

– Designed to work for hydrogen atom only. Other elements/substances are much more complicated

– Electrons are not merely particles circling the nucleus of atoms, they exhibit wave-like properties

Section 6

.3

• Do the following transitions represent absorption of energy or emission of energy:– n = 3 to n = 1?

– n = 2 to n = 4?

Section 6

.4

• DeBroglie Equation: Relationship

between mass and wavelength:

=h

mv

= wavelength (meters)

h = Planck’s constant (6.63 × 10–34 J·s)

m = mass (kg)

v = velocity (meters/s) Reminder: 1 J = 1 kg·m2/s2

• Louis de Broglie suggested that if light

(photons) has material properties, then

matter should exhibit wave properties.

Section 6

.4

• Calculate the velocity of a neutron whose de Broglie wavelength is 500 pm.

(Neutron mass = 1.675 x 10–24 g)

Section 6

.4

• The more precisely the momentum (mv) of a particle

is known, the less precisely its position (x) is known

(and vice versa):

• The uncertainty of an electron’s position can be greater

than the size of the atom! (see pg 225!)

(x)(mv) h

4

Section 6

.4

• Use a camera to photograph a car in motion.

• Short exposure shot: good idea of the car’s position, but not of it’s speed

• Long exposure shot: good idea of speed, but position is blurry

Section 6

.4

• Doesn’t apply to large objects (e.g. a

tennis balls or people) because

(x)(mv) is much smaller than the

size of the object.

m

smkg

Js

vm

hx 34

34

1006.4/894.0145.04

10626.6

4

m

smkg

Js

vm

hx 9

431

34

101/10510109.9

10626.6

4

Baseball (d=0.075m) at 90 mph with an uncertainty of 2 mph:

Electron at (d=<10-10m) at a bit over 1million mph with uncertainty of a bit over 100,000 mph:

Section 6

.4

• Quantum mechanics -

mathematical treatment into which

both the wave and particle nature

of matter is incorporated

• Developed by Erwin Schrödinger

As we delve deeper into the atom, it actually becomes

less tangible and more mathematical.

Section 6

.5

• The “wave” equation is

designated with a lower

case Greek psi ().

• The square of this

equation,2, gives a

probability density map.

Section 6

.5

– More blue dots = more likely to be there

– This tells us where an

electron is statistically likely

to be at any given instant.

• Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies.

• Orbitals describe a spatial distribution of electron density (90% probability of finding a particular electron or electrons).

• Quantum numbers are used to describe each orbital. A total of three quantum numbers is required to describe a specific orbital.

Section 6

.5

• The principal quantum number, n, describes the energy level on which the orbital resides.

• The values of n are whole numbers > 0.

– e.g. n = 1, n = 2, n = 3, etc

– Same n as in the Bohr model

– n is equal to the number of the row on the periodic table

Section 6

.5

• The azimuthal quantum number, l (“ell”), defines the

shape of the orbital.

• Possible values for l: integers ranging from 0 to n−1.

• Letter designations of l are used to describe the

different values (i.e. shapes) of orbitals.

Value of l 0 1 2 3

Type of orbital s p d f

Section 6

.5

• The magnetic quantum number, ml, describes the three-dimensional orientation of the orbital.

• Possible values are integers ranging from +l to –l(including zero):

-l ≤ ml ≤ +l

Example: l = 1 ml = -1, 0, +1 (3 values)

• Therefore, on any given energy level (n), there can be up to: – 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.

which of these are available depends on n and then l.

Section 6

.5

• All the orbitals with the same value of n form a shell.

• Different orbital types within a shell are subshells.

Section 6

.5

• A shell with principal

quantum number n has

exactly n subshells

– n=2 2 subshells (l=0, l=1)

• Each subshell has 2l+1

orbitals – l=0 ml=0

– l=1 ml=1,0,-1

• The total number of

orbitals in a shell is n2.– n=2 4 (count ml values)

Section 6

.5

Each box represents

1 orbital

Each group represents 1 subshell

Each row represents

1 shell

• Predict the number of subshells in the fourth shell (n=4).

• Give the label for each of these subshells.

• How many orbitals are in each of these subshells?

Section 6

.5

• Value of l = 0.

• Spherical in shape.

• Radius of the sphere

increases as n increases.

– rn=1<rn=2<rn=3< …

Section 6

.6

The s orbitals possess n−1 nodes, or regions where

there is zero probability of finding an electron.

Section 6

.6

• Value of l = 1.

• Two lobes with 1 node between them.

• ml = –1, 0, +1 and thus 3 different spatial orientations

For convenience we place the lobes along the x, y and z axes.

Section 6

.6

• Value of l is 2; five values of ml (+2, +1, 0, –1, –2)

• Four of the five orbitals have 4 lobes; the other

resembles a p orbital with a ring around the center.

Section 6

.6

• For a one-electron

hydrogen atom, orbitals

on the same energy level

have the same energy

(degenerate).

• But this is only theory,

what we observe is…

Section 6

.7

• As the number of

electrons increases,

so does the repulsion

between them.

• In many-electron

atoms, orbitals in the

same energy level are

no longer degenerate.

Specific orbitals are described by n, l and ml, but 2 electrons

can be located in an orbital. How can we distinguish them?

Orbitals in the same subshell

are degenerate

Section 6

.7

• In the 1920s, it was found that two electrons in the

same orbital do not have exactly the same energy.

• The “spin” of an electron describes its magnetic field,

which affects its energy.

Section 6

.7

• This led to a 4th quantum

number, the spin quantum

number, ms.

• The spin quantum number

has only 2 allowed values:– ms = +½ or ms = −½.

• No two electrons in the same atom can have exactly the same energy.

• No two electrons in the same atom can have four identical quantum numbers.

• Each orbital can only hold two electrons (and they must have opposite spins, ms = +½, –½).

Section 6

.7

• Each electron’s “address” is a unique combination of the 4 quantum numbers

No two orbitals can have the exact same n, l, and ml values!

No two electrons can have the exact same n, l, ml, and ms

values!

Symbol Name Description Values Misc. notes

n principal Energy level of orbital

Integers > 0 n corresponds to a row on periodic table

l azimuthal(angular)

Shape of orbital Integers 0 to n–1

0 = s 1 = p2 = d 3 = f

ml Magnetic 3D orientation of orbital

Integers–l to +l

Gives number of orbitals for different

values of l

ms Spin Electron spin +½, –½ Only describes electrons, not orbitals

Section 6

.7

• Consists of

– Number denoting the energy

level. Corresponds to principle QN, n

– Letter denoting the type of

orbital. Corresponds to azimuthal QN, l

– Superscript denoting the

number of electrons in those

orbitals.

4p5

Section 6

.8

• Tally of where each electron is in an atom.

• What is the designation for the subshell with n=5 and l=1?

• How many orbitals are in this subshell?

• Indicate the values for ml for each of these orbitals.

Section 6

.7

• Write the electron configuration for Li atom.

Section 6

.7

• Each box represents one orbital.

• Half-arrows represent the electrons.

• The direction of the arrow represents the spin of

the electron.

• Orbital diagrams represent the “ground state” or

most stable electron configuration

Section 6

.8

“For degenerate orbitals, the lowest energy is

attained when the number of electrons with the

same spin (ms) is maximized.”

Don’t pair up electrons until after you’ve half-filled a subshell.

Nitrogen has 7 electrons:

Section 6

.8

• Draw the orbital diagram for the electron configuration of oxygen (atomic number 8).

• How many unpaired electrons does an oxygen atom have?

Section 6

.7

• Write the full electron configuration for P, element 15.

• How many unpaired electrons does a P atom possess?

Section 6

.8

• Fill orbitals in increasing order of energy

• Rows correspond to principal quantum numbers

• Groups correspond to different electron configurations.

s1 s2

s2… p1 p2 p3 p4 p5 p6

d1 d2 d3….s2…n = 1

n = 2n = 3n = 4n = 5n = 6n = 7

Section 6

.8

1s

2s 2p

3s 3p 3d

4s 4p 4d 4f

5s 5p 5d 5f 5g

6s 6p 6d 6f 6g 6h

7s 7p 7d 7f 7g 7h 7i

8s

Same order as previous slide

Elements with orbitals in lighter

shade aren’t known (yet!)

Filling from lowest to

highest energy level

is called the Aufbau

Principle

Section 6

.8

• Not sure which orbitals are lowest energy? – Fill lowest sum of n+l first

– Ties go to lower n

• What order should we fill

– Check n+l what order should we fill 3d, 4s & 4p?

3d: n=3, l=2 n+l =5

4s: n=4, l=0 n+l =4

4p: n=4, l=1 n+l =5

• Fill order: 4s, 3d, 4p

Section 6

.8

• Group 8A elements are said to have “filled shells”.

• Filled shell electrons are called “core electrons” and do

not participate in making bonds or redox reactions.

• Electrons in the “outer shell” are “valence electrons” and

do participate in bonding and redox reactions.

• We write condensed electron configurations by writing

the next lowest noble gas configuration (the core

electrons) plus the valence electrons

• Examples: P – 1s22s22p63s23p3 [Ne]3s23p3

Ge – 1s22s22p63s23p34s23d104p2

[Ar]4s23d104p2

Section 6

.8

• Write the condensed electron configuration for Te (element 52).

Section 6

.9

• Which element has an electron configuration of [Kr]5s24d3 ?

• How many unpaired electrons are there in this element?

Section 6

.9

• For predicting reactivity, the

valence shell configuration is

most important.

Section 6

.9

S

– We don’t usually consider

electrons in completely filled d

or f subshells

• What family of elements is characterized by

an ns2np2 electron configuration in the

outermost occupied shell?

• What family of elements is characterized by

an ns2np5 electron configuration in the

outermost occupied shell?

Section 6

.9

• 4s and 3d orbitals are very close in energy

• Energetically favorable to half-fill or fully fill the d orbitals

Section 6

.9

• Similar logic also applies to the f-block

Order of orbital stability 1. Full or empty subshell 2. Half –filled 3. Everything else

• If the energy

cost very low,

re-arrange to

make more

stable

subshells

Section 6

.9

Chromium: [Ar] 4s13d5

not [Ar] 4s23d4

Copper: [Ar] 4s13d10

not [Ar] 4s23d9

4s 3d

Full + Random

½ Full + Full

More Stable

• When writing electron configurations remember: 1. Fill lowest energy levels first (Aufbau Principle)

Lowest sum of n+l goes first

Ties go to the lowest n

2. Limited to 2 electrons per orbital so s subshell gets 2 max

p subshell gets 6 max

d subshell gets 10 max

f subshell get 14 max

3. Be aware of anomalies Above 4s, bump an electron up to the d or f

subshell if doing so will create a combination of full,

empty or half-filled shells.

Chapte

r 6

• Calculations involving E, l, n, m and v

• Bohr hydrogen atom model

• Electron transitions and Rydberg equation

• Energy states

• Strengths and limitations of the model

• DeBroglie equation, uncertainty principle (define

and calculate)

• What are orbitals and probability densities?

Chapte

r 6

• Quantum numbers, orbital shapes, shells,

subshells, and nodes

• Ordering of orbitals: degenerate vs non-

degenerate, Pauli exclusion principle

• Writing electron configurations, Hund’s rule,

condensed electron configurations, electron

configurations of groups on periodic table

Chapte

r 6